Answer:
The equation of the line is;
[tex]y=-2x+3[/tex]Explanation:
Given that
the slope of a line is -2 and it passes through the point (4,-5).
Applying the slope-intercept form of equation;
[tex]y-y_1=m(x-x_1)[/tex]Substituting the values of the slope and coordinates;
[tex]\begin{gathered} y-(-5)=-2(x-4) \\ y+5=-2x+8 \\ y=-2x+8-5 \\ y=-2x+3 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-2x+3[/tex]Answer:
2x + y = 3
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 5 ) into the partial equation
- 5 = - 8 + c ⇒ c = - 5 + 8 = 3
y = - 2x + 3 ← in slope- intercept form
add 2x to both sides
2x + y = 3 ← equation in standard form
What is the length of the dotted line in the
diagram below? Round to the nearest
tenth.
Answer: Length = 10√2
Step-by-step explanation: You have to use the pythagorean theorem
REVIEW & REFRESH
42. Tell whether x and y are proportional.
43. What number is 60% of 35?
44. 27 is what percent of 75?
Just do 42 and 44
Using proportions, it is found that:
42. x and y are not proportional.
43. The number 21 is 60% of 35.
44. The number 27 is 36% of the number 75.
How to verify if two variables are proportional?Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.
From the table, the ratios are given as follows:
6/4 = 1.5.8/6 = 1.25.Different ratios, hence the variables x and y are not proportional.
Percentage of a numberTo find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.
The decimal equivalent of a percentage of 60% is:
60/100 = 0.6.
Hence the percentage of 35 is calculated as follows:
0.6 x 35 = 21.
The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:
27/75 x 100% = 36%.
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A groundskeeper needs grass seed to cover a circular field 290 ft in diameter a store sells 50-pound bags of grass seed. One pound of grass seed covers about 400 square ft. What is smallest number of bags there groundskeeper must buy to cover the circular field
Using the concept of area, we got 165 bags is the smallest number of bags there groundskeeper must buy to cover the circular field.
The branch of mathematics which deals with measuring is known as Mensuration. It was basically first used for land surveys and other civic works in Egypt. The father of mensuration is known as Archimedes. Mensuration is a discipline of mathematics which studies the measurements of various geometrical forms possible and their areas, perimeters, and volumes, among other things.
Diameter of the field = 290 feet, radius = 145 feet
Area of the circular field =[tex]\pi r^{2}[/tex]
=>[tex]\pi[/tex]×145×145 =66018.5 square feet.
No of bags to be brought = 66018.5/400=165bags,
Hence, the smallest number of bags is 165 which groundskeeper must buy to cover the circular field.
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Malika buys 20 bottles of cranberry juice at the corner store for a total cost of $20. If each bottle costs the same amount, how much is each bottle of juice?
Answer: 1 dollar per bottle
Step-by-step explanation:
If they cost $20 and she bought 20 bottles, we can use division.
$20 / 20 bottles = 1 dollar per bottle
On the map, 0.1 inches represents
25 miles. If the real distance between
two cities is 112.5 miles, what is the
distance between their locations on
the map?
A. 0.45 in
B. 2 in
C. 0.2 in
D. 1 in
The distance between the two cities on the map is 0.45 inches , the correct option is (A) 0.45inches .
In the question ,
it is given that
the scale factor of the map is 25 miles = 0.1 inches
So, 1 mile = 0.1/25 inches
= 0.004 inches
So , on the map 1 mile is represented by 0.004 inches
Given that the real distance between the two cities is 112.5 miles
So , on the map 112.5 miles = 112.5*0.004 inches
= 0.45 inches
Therefore , the distance between the two cities on the map is 0.45 inches , the correct option is (A)0.45inches .
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. The population of Star, ID was 1800 people in the year 2000. The population has been growing at a rate of 9.9% annually. a. Write a function that models the population of Star, ID in years since 2000.b. Use your function to predict the population of Star, ID in 2050.c. The function g(x)=11000(1.056)^x models the population of Eagle, ID in years (x) since 2000. Which city is growing faster? How do you know?
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
Part A:
The function that models the population of Star, ID in years since 2000 is:
[tex]f(x)\text{ = 1800 }(1\text{ + }\frac{9.9}{100})^t[/tex]Part B :
Use your function to predict the population of Star, ID in 2050
[tex]\begin{gathered} \text{Given } \\ f(x)\text{ = 1800 ( 1 + }\frac{9.9}{100}^{})^t \end{gathered}[/tex]The year 2050 means that t= 50, we have that:
[tex]\begin{gathered} f(x)=\text{ 1800 ( 1 + }\frac{9.9}{100})^{50} \\ f(x)=1800X(1+0.099)^{50} \\ f(x)\text{ =}1800(1.099)^{50} \\ f(x)=201,909.6734 \\ f(x)\approx\text{ 201, 910 ( to the nearest whole number)} \end{gathered}[/tex]Part C:
The function:
[tex]g(x)\text{ = 11000 ( 1}.056)^x[/tex]models the population of Eagle, ID in years (x) since 2000.
Which city is growing faster? How do you know?
Answer:
From this equation, we can see that the growth rate is 5.6% annually.
Comparing this, with the initial function:
[tex]f(x)=1800(1.099)^{50}[/tex]We can see that the annual growth rate of f(x) is 9.9 %
CONCLUSION:
The population of Star ID, with the function, g (x) has a faster growth rate.
2) Choose the correct answer.
A given line passes through the points (2, 3) and (2, 3). Determine the equation of the
line that is perpendicular to the given line and passes through the point (1,5).
y = 5
x = -1
x=5
y= -1/2x + 13/3
y = -1
There is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
What is meant by equation?The definition of an equation in algebra exists as a mathematical statement that demonstrates the equality of two mathematical expressions.The equation of a perpendicular line to a line in point-slope form is expressed as:
y - y1 = -1/m(x - x1)m is the slope(x1, y1) is any point on the lineDetermine the slope:
Slope = -3-3/2-2y = ∞Since there is no slope, hence the equation of the line will be in the form y = b.
Where b exists the y-coordinate of the point. Hence the required equation of the line is y = 5Therefore, there is no slope, hence the equation of the line will be in the form y = b. Then the equation of the line that is perpendicular to the given line and passes through the point (1, 5) exists (A) y = 5.
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Correct question:
2) Choose the correct answer.
A given line passes through points (2, 3) and (2, 3). Determine the equation of thethe line that is perpendicular to the given line and passes through the point (1,5).
(A) y = 5
(B) x = -1
(C) x=5
(D) y= -1/2x + 13/3
(E) y = -1
-3/2x = 6 solve for x and simplify your answer as much as possible
Answer: x = -4
Step-by-step explanation:
Multiply both sides by 2 to get:
-3x = 12
Then, divide both sides by -3 to get:
x = -4
Hope this helps!
Answer:
x = -4
Step-by-step explanation:
(Order of Operations with Radicals LC)
Simplify the expression.
square root of 49 minus 2 squared
Answer:
3Step-by-step explanation:
Given expression[tex]\sqrt{49}-2^2[/tex]Simplify it as follows[tex]\sqrt{49}-2^2 =[/tex][tex]7-4=[/tex][tex]3[/tex]Answer:
3
Step-by-step explanation:
i got it right on the exam!
Where do I put the dots at
If a and b are two events defined on the same sample space, given that p(a) = 0.28 and p(aub) =0.51, find the p(b) such that a and b are mutually exclusive
The possibility of an event or outcome happening contingent on the occurrence of a prior event or outcome is known as conditional probability. The probability of the prior event is multiplied by the current likelihood of the subsequent, or conditional.
Occurrence to determine the conditional probability. P(A and B) = P(A) * P if A and B are two Independent events (B).
How can you calculate the likelihood of two occurrences, A and B, coming together?
The probability of their union, or the event that either A or B occurs, is equal to the total of their probabilities less the sum of their intersection if two occurrences A and B are not disjoint. P(A) + P(B) - P(A and B) (A and B).
The answer is then (0.28 + P(B) - (0.51 = 0.23).
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When radioactive substances decay, the amount remaining will form a geometric sequence when measured over constant intervals of time. The table shows the amount of a radioactive isotope initially and after 2 hours. What are the amounts left after 1 hour, 3 hours, and 4 hours?
Answer:
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
Explanation:
To find the amount left after 1 hour, 3 hours, and 4 hours, we need to find the common ratio.
Since we know the initial amount and the amount left after 2 hours, the ratio of these quantities is the square of the common ratio, so
r² = 537/1986
r² = 0.2704
r = √0.2704
r = 0.52
Then, the amount left after 1 hour is the initial amount multiplied by the common ratio, so
For 1 hour
Amount left = 1986(0.52) = 1032.7 grams
In the same way, the amount left after 3 and 4 hours is
For 3 hours
Amount left = 537(0.52) = 279.2 grams
For 4 hours
Amount left = 279.2(0.52) = 145.2 grams
Therefore, the complete table is
Hour elapsed 0 1 2 3 4
Grams 1986 1032.7 537 279.2 145.2
A ball was dropped from the Empire State Building observatory. The height of the ball in feet is described by the function f(x) = 1048 - 16[tex]x^{2}[/tex], where x is the time in seconds.
Find the inverse function [tex]f^{-1}[/tex](x) and explain its meaning.
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] is the inverse function and it means the time in seconds it will take the ball to attain a certain height in feet.
What is the inverse function f^-1(x) and its meaning?
Given:
[tex]f(x) = 1048 - 16x^{2}[/tex]
Since the function f(x) is the height (h), we can write the function as :
[tex]h = 1048 - 16x^{2}[/tex]
We will make x the subject:
[tex]16x^{2} = 1048 - h[/tex]
[tex]x^{2} = \frac{1048 - h}{16}[/tex]
[tex]x = \sqrt{\frac{1048 - h}{16} }[/tex]
[tex]x = \sqrt{65.5 - 0.0625h }[/tex]
Since:
[tex]x = f^{-1} (h) = \sqrt{65.5 - 0.0625h }[/tex]
Thus:
[tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex]
Therefore, the inverse function is [tex]f^{-1} (x) = \sqrt{65.5 - 0.0625x }\\[/tex] and it is a function describing the amount of time (in seconds) it takes for the ball to reach a height of h feet.
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What is the midpoint of a segment with endpoints at (-4.-8) and (8.10)? O A. (-6,-9) OB. (-6,1) OC. (2,-9) OD. (2,1)
Answer
Option D is correct.
Midpoint = (2, 1)
Explanation
The midpoint of two coordinates is obtained by respective x-coordinates together and dividing by 2 and then doing similarly for the y-coordinate.
(-4, -8) and (8, 10)
Midpoint = (x, y)
x = (-4 + 8)/2 = (4/2) = 2
y = (-8 + 10)/2 = (2/2) = 1
Hope this Helps!!!
Rewrite expression (4^-2)^3 using positive exponents
The positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
The given expression is [tex](4^{-2})^3[/tex].
What is a positive exponent?A positive exponent tells us how many times to multiply a base number, and a negative exponent tells us how many times to divide a base number. We can rewrite negative exponents like x⁻ⁿ as 1 / xⁿ.
The given expression can be simplified as follows
[tex](4^{-2})^3[/tex] = [tex]4^{-2\times3}=4^{-6}[/tex]
So, the positive exponent = [tex]\frac{1}{4^6}[/tex]
Therefore, the positive exponent for the given expression is [tex]\frac{1}{4^6}[/tex].
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The marked price of an article is Rs.2080. After allowing d% discount and levying(d-2)% VAT,the cost of the article becomes Rs 1997.84. find the discount amount and VAT amount
The discount rate is 15% and the VAT rate is 13%
What is the value of the discount?The following can be deduced:
MP = 2080
Discount = d%
VAT = (d-2)%
Cost = 1997.84
Apply discount:
2080 - d% = 2080*(1 - 0.01d)
Add VAT:
2080*(1 - 0.01d) + (d - 2)%
2080*(1 - 0.01d) * (1 + (d -2)/100)
2080*(1 - 0.01d) * (0.98 + 0.01d)
= 1997.84
(1 - 0.01d)(0.98 + 0.01d) = 1997.84/2080
0.98 + 0.01d - 0.0098d - 0.0001d²
= 0.9605
- 0.0001d² + 0.0002d + 0.98- 0.9605 = 0
0.0001d²- 0.0002d - 0.0195 = 0
d² - 2d + 195 = 0
Solving the quadratic equation we get:
d = 15
Therefore discount is 15%
VAT rate = d - 2 = 15% - 2% = 13%
The concept shown above is the calculation for the discount and the amount of the value added tax.
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2. Write three decimals that
have a sum of 114.056.
Three decimal that sum of 114.056 is 52.2+34.15+28.5.
What is decimal?
decimal is a term that describes the base-10 number system, probably of the most commonly used the number system. The decimal number system of consists of ten single-digit numbers.
We will represent this as 1.5 pizzas in decimal form. In this case, the dot stands in for the decimal point, the number before the dot, in this case "1," represents one whole pizza, and the number after the decimal point, or the fractional part, represents the other half of the pizza. You may have seen decimal numbers similar to these while grocery shopping, on a scale, or even during a baseball game.
Sol- we have to add three decimal that have a sum of 114.056 no parts are given here.
Let's take
X+Y+Z = 114.056
We need to add any particular number here
Let's put 52+34+28
Still we need .056 extra
So we have to add points here
52.2+34.15+28.5
So these are 3 decimal point.
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an automated weight monitor can detect underfilled cans of beverages with probability 0.98. what is the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled can?
The probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
What is probability?
Probability is defined as the possibility of an event to occur.
An automated weight monitor can detect underfilled cans of beverages with probability [tex]0.98[/tex]
Thus probability of success will be [tex]p=0.98[/tex]
So probability of failure [tex]q=1-p=1-0.98=0.02[/tex]
To find the first wrong detection happening on the tenth trial the first nine trials must be success followed by failure in the tenth trial.
Thus, required probability [tex]=p^9q^1=(0.98)^9(0.02)=0.01667496[/tex]
Hence the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled is [tex]0.01667496[/tex].
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what is BIDMAS?
Please answer
Answer:
BIDMAS is a math term that is used to describe these 6 terms.
Brackets
Indices, which is another word for exponents
Division
Multiplication
Addition
Subtraction
Answer:
It is the order of operation in order to know how to calculate an equation starting from which order.
Step-by-step explanation:
Brackets first
Indices second
Division and multipaction third. From left to right
Addition and subtraction last. From left to right
The numbered disks shown are placed in a boxand one disk is selected at random. Find theprobability of selecting an odd number, given that agreen disk is selected.Find the probability of selecting an odd number, given that a green disk is selected.(Type an integer or a simplified fraction.)
Given that the numbered disks are placed in a box, you need to find the probability of selecting an odd number, given that a green disk is selected.
Therefore, you need to use the Conditional Probability Formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]In this case, let be "A" the event of selecting an odd number, and "B" the event of selecting a green disk.
You can identify that:
- There are a total of 8 disks.
- There are 4 green disks that have odd numbers.
- There are a total of 7 green disks.
Therefore, you can determine that:
[tex]P(A\cap B)=\frac{4}{8}=\frac{1}{2}[/tex]And:
[tex]P(B)=\frac{7}{8}[/tex]Then, you can substitute values into the formula and evaluate:
[tex]P(A|B)=\frac{\frac{1}{2}}{\frac{7}{8}}=\frac{1\cdot8}{2\cdot7}=\frac{8}{14}=\frac{4}{7}[/tex]Hence, the answer is:
[tex]\frac{4}{7}[/tex]4(8g+5)+6
I thought the answer was 32g+26 but its not on there
Answer:
32g + 6(you got it right, not quite sure why it isn't there though!)
Step-by-step explanation:
remember PEMDAS
parentheses first
(8g+5) but we can't add them up since they not like terms
now we go from left to right (since we have Multiplication first and then Addition)
distribute the 4 to the (8g+5)
which makes it 32g +20
now we go back to the equation,
32g +20 + 6
are there any like terms we can combine?
yes, the 20 and the 6
20+6=26
leaving us with
32g + 26Two large and 1 small pump can fill a swimming pool in 4 hours. One large and 3 small pumps can also fill the same swimming pool in 4 hours. How many hours will it take 4 large and 4 small pumps to fill the swimming pool?
Answer: It will take just 1 hour & 36 minutes with 4 large pumps & 4 small pumps
Step-by-step explanation:
EEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEE
Answer:
c = 23
Step-by-step explanation:
To start, the interior of ∠L is needed to complete the equation. Since the total value of an interior and exterior angle is equal to 180°, we can confirm that 180° - 83° = 97°. Now, we can plug in the numbers.
(2c + 51)° = 97°
Next, you want to subtract 51 from both sides.
(2c + 51) - 51 = 97 - 51
2c = 46
Lastly, you isolate c by dividing 46 by 2.
c = 46 ÷ 2
c = 23
“Order these numbers from smallest to largest: 2/3, 7/8, 0.5, 2/5. Justify your answer”
Step 1
Given
[tex]\frac{2}{3},\frac{7}{8},\frac{1}{2}\text{ and }\frac{2}{5}[/tex]Required: To arrange them from smallest to largest.
Note: 0.5 = 1/2
Step 2
Find the lowest common multiple of the numbers in the denominator : 3,8,2 and 5
Hence, the lowest common multiple will be
[tex]2\times2\times2\times3\times5\text{ = 120}[/tex]Step 3
Use the LCM to arrange the numbers as seen below
From the numbers gotten from using the LCM, we can now conclude
Step 4
Arrange them from smallest to largest
[tex]\begin{gathered} \text{From the size of the numbers related to the image above,} \\ 80->\frac{2}{3},\text{ 105}\to\frac{7}{8},\text{ 60}\to\frac{1}{2},\text{ 48}\to\frac{2}{5} \end{gathered}[/tex]We can arrange them as follows
[tex]\frac{2}{5},\frac{1}{2},\frac{2}{3},\frac{7}{8}[/tex]Question 5
Fill in the blank question.
Jack wants to buy a coat that costs $74.95. The sales tax rate in his city is 612% . What is the total cost for the coat?
The coat has a total cost of $533.644
How to determine the total cost for the coat?From the question, the given parameters are:
Cost of a coat = $74.95
Sales tax in the city = 612%
Using the sales tax, the total cost for the coat is calculated using
Total cost of coat = Cost of a coat + Cost of a coat * Sales tax in the city
Substitute the known values in the above equation
So, we have the following equation
Total cost of coat = 74.95 + 74.95 * 612%
Evaluate the products
Total cost of coat = 74.95 + 458.694
Evaluate the sum
Total cost of coat = 533.644
Hence, the total cost of the coat is $533.644
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Calvin wants to sell a basic badminton kit to his friends. In that kit, he puts two rackets worth
140 each and a shuttlecock worth 280. He wants to have a profit of 25%.
For how much should Calvin sell the kit?
Answer:
realto, hindi ako sure eh
Step-by-step explanation:
tama yan
PLEASE HELP ASAP (100 POINTS) If the line of best fit is y = 1.416x − 0.76, what is the residual value for the coordinate (7, 8)?
A. −1.152
B. 1.152
C. −3.568
D. 3.568
Answer:
A: -1.152Step-by-step explanation:
y = 1.416x − 0.76
For (7, 8):
residual value = Measured value - Predicted value
residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)
When x = 7:
value of y from the equation, y1 = 1.416*7 - 0.76
y1 = 9.912 - 0.76
y1 = 9.152actual y-coordinate of the point, y2 = 8
From:
residual value = (actual y-coordinate of the point, y2) - (value of y from the equation, y1)
residual value = y2 - y1
residual value = 8 - 9.152
residual value = -1.152Answer:
A: -1.152
Step-by-step explanation:
I did it and it was right!
As a Nurse, part of your daily duties is to mix medications in the proper proportions for your patients. For one of your regular patients, you always mix Medication A with Medication B in the same proportion. Last week, your patients doctor indicated that you should mix 130 milligrams of Medication A with 117 milligrams of Medication B. How many milligrams of Medication A should be mixed this week?
60 milligrams of medication A should be used this week
Explanation:Given:
Last week, 130 milligrams of Medication A was mixed with 117 milligrams of Medication B
This week, 54 milligrams of medication B was used
To find:
the milligrams for medication A used this week
To determine the milligrams of medication A used, we will apply the ratio of medication A to B
Last week:
A : B = 130 : 117
This week:
A : B = A : 54
[tex]\begin{gathered} eqating\text{ both ratios:} \\ A:B\text{ = A : }B \\ 130:\text{ 117 = A :}54 \\ \\ \frac{130}{117}=\text{ }\frac{A}{54} \\ cross\text{ multiply:} \\ 130(54)\text{ = 117\lparen A\rparen} \end{gathered}[/tex][tex]\begin{gathered} A=\text{ }\frac{130\times54}{117} \\ A=\text{ 60} \end{gathered}[/tex]Hence, 60 milligrams of medication A should be used this week
The gumball machine contains 9 red,7 white and 8 blue gumballs. find the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.
The person must buy 10 gumballs so that she gets 4 gumballs that are the same color.
Given, gumball machine contains 9 red gumballs
7 white gumballs and
8 blue gumballs.
we are asked to determine the least number of gumball a person must buy to be sure that she gets 4 gumballs that are the same color.
If a person gets three gumballs of each of the three colors, that is, 9 gumballs, then the 10th gumball must be the fourth one for one of the colors. Therefore, the person must buy 10 gumballs.
Hence 10 gumballs should be purchased.
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2/3x - 8 when x = 12
1) For this question, all we need to do is to plug it in the value for x.
So,
2/3x -8 =0 Plugging into x the value x=12
2/3(12) -8 =0
8 -8 =0
0
So when x=12, then the equation is equal to zero. This leads us to conclude that 12 is the root or the solution of this equation.